101 LearnersLast updated on May 26th, 2025
Factors of 1656
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 1656, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1656?
The numbers that divide 1656 evenly are known as factors of 1656. A factor of 1656 is a number that divides the number without remainder. The factors of 1656 are 1, 2, 3, 4, 6, 8, 12, 24, 69, 138, 276, 552, 828, and 1656. Negative factors of 1656: -1, -2, -3, -4, -6, -8, -12, -24, -69, -138, -276, -552, -828, and -1656. Prime factors of 1656: 2 and 3. Prime factorization of 1656: 2^3 × 3 × 23. The sum of factors of 1656: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 + 69 + 138 + 276 + 552 + 828 + 1656 = 3579
How to Find Factors of 1656?
Factors can be found using different methods. Mentioned below are some commonly used methods: Finding factors using multiplication Finding factors using division method Prime factors and Prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1656. Identifying the numbers which are multiplied to get the number 1656 is the multiplication method. Step 1: Multiply 1656 by 1, 1656 × 1 = 1656. Step 2: Check for other numbers that give 1656 after multiplying: 2 × 828 = 1656 3 × 552 = 1656 4 × 414 = 1656 6 × 276 = 1656 8 × 207 = 1656 12 × 138 = 1656 24 × 69 = 1656 Therefore, the positive factor pairs of 1656 are: (1, 1656), (2, 828), (3, 552), (4, 414), (6, 276), (8, 207), (12, 138), and (24, 69). For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers by whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following the simple division method: Step 1: Divide 1656 by 1, 1656 ÷ 1 = 1656. Step 2: Continue dividing 1656 by the numbers until the remainder becomes 0. 1656 ÷ 1 = 1656 1656 ÷ 2 = 828 1656 ÷ 3 = 552 1656 ÷ 4 = 414 1656 ÷ 6 = 276 1656 ÷ 8 = 207 1656 ÷ 12 = 138 1656 ÷ 24 = 69 Therefore, the factors of 1656 are: 1, 2, 3, 4, 6, 8, 12, 24, 69, 138, 276, 552, 828, and 1656.
Prime Factors and Prime Factorization
The factors can be found by dividing with prime numbers. We can find the prime factors using the following methods: Using prime factorization Using factor tree Using Prime Factorization: In this process, prime factors of 1656 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1. 1656 ÷ 2 = 828 828 ÷ 2 = 414 414 ÷ 2 = 207 207 ÷ 3 = 69 69 ÷ 3 = 23 23 ÷ 23 = 1 The prime factors of 1656 are 2, 3, and 23. The prime factorization of 1656 is: 2^3 × 3 × 23.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show: Step 1: Firstly, 1656 is divided by 2 to get 828. Step 2: Now divide 828 by 2 to get 414. Step 3: Then divide 414 by 2 to get 207. Step 4: Divide 207 by 3 to get 69. Step 5: Divide 69 by 3 to get 23. Here, 23 is a prime number that cannot be divided anymore. So, the prime factorization of 1656 is: 2^3 × 3 × 23. Factor Pairs Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs. Positive factor pairs of 1656: (1, 1656), (2, 828), (3, 552), (4, 414), (6, 276), (8, 207), (12, 138), and (24, 69). Negative factor pairs of 1656: (-1, -1656), (-2, -828), (-3, -552), (-4, -414), (-6, -276), (-8, -207), (-12, -138), and (-24, -69).
Common Mistakes and How to Avoid Them in Factors of 1656
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are factors for every number. Always remember to include 1 and the number itself. For example, in factors of 1656, 1 and 1656 are also factors.
Factors of 1656 Examples
Problem 1
There are 12 friends and 1656 candies. How will they divide them equally?
They will get 138 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends. 1656/12 = 138
Problem 2
A garden is rectangular, the length of the garden is 69 meters and the total area is 1656 square meters. Find the width?
24 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width 1656 = 69 × width To find the value of width, we need to shift 69 to the left side. 1656/69 = width Width = 24.
Problem 3
There are 6 boxes and 1656 marbles. How many marbles will be in each box?
Each box will have 276 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the number of boxes. 1656/6 = 276
Problem 4
In a school, there are 276 students, and 6 classes. How many students are there in each class?
There are 46 students in each class.
Explanation
Dividing the students by the total classes, we will get the number of students in each class. 276/6 = 46
Problem 5
1656 apples need to be placed in 8 baskets. How many apples will go in each basket?
Each basket will have 207 apples.
Explanation
Divide total apples by baskets. 1656/8 = 207
FAQs on Factors of 1656
1.What are the factors of 1656?
2.Mention the prime factors of 1656.
3.Is 1656 a multiple of 4?
4.Mention the factor pairs of 1656?
5.What is the square of 1656?
Important Glossaries for Factor of 1656
Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1656 are 1, 2, 3, 4, 6, 8, 12, 24, 69, 138, 276, 552, 828, and 1656. Prime factors: The factors which are prime numbers. For example, 2, 3, and 23 are prime factors of 1656. Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 1656 are (1, 1656), (2, 828), etc. Prime factorization: The expression of a number as a product of its prime numbers. For example, the prime factorization of 1656 is 2^3 × 3 × 23. Multiplication method: A method used to find factor pairs by multiplying numbers to get the target number, such as finding pairs for 1656.
Explore More numbers
Previous to Factors of 1656
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
